Problem: The tangent line to the graph of function $f$ at the point $(2,3)$ passes through the point $(7,6)$. Find $f'(2)$. $f'(2)=$
Explanation: The derivative of a function at a point gives the slope of the line tangent to the function's graph at that point. Therefore, $f'(2)$ gives the slope of the tangent line to the graph of $f$ where $x=2$, which is the point $(2,3)$. We know this line passes through $(2,3)$, and we are also given that it passes through $(7,6)$. This should be enough to find the slope of that line. $\begin{aligned} \text{Slope}&=\dfrac{\text{Change in }y}{\text{Change in }x} \\\\ &=\dfrac{6-3}{7-2} \\\\ &=\dfrac{3}{5} \end{aligned}$ In conclusion, $f'(2)=\dfrac{3}{5}$.